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3 years ago

A number increased by 10 is 114

Mathematics

2 answers:

motikmotik3 years ago

8 0

104 is the number because 114-10=104

sesenic [268]3 years ago

4 0

104 plus 10 equals 114

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The height of a tree at time t is given by a twice-differentiable function H, where H(t) is measured in meters and t is measured

il63 [147K]

A) Use the mean value theorem.

$H'(6)\approx\dfrac{H(7)-H(5)}{7-5}=\dfrac{11-6}2=\dfrac52\text{ meters/year}$

Since $H(t)$ gives the tree's height in meters at time $t$ , the value of $H'(6)$ informs us how quickly the tree is growing exactly after 6 years have passed. (i.e. the instantaneous rate of change of the tree's height)

b) We use the mean value theorem again. Observe that $H(5)-H(3)=6-2=4$ , and that $5-3=2$ . By the MVT, there must be some $3$ such that

$H'(t)=\dfrac42=2$

c) The average height of the tree is given by the integral

$\displaystyle\frac1{10-2}\int_2^{10}H(t)\,\mathrm dt$

If you can remember the formula for the area of a trapezoid, then this is pretty easy to compute. With five data points, you end up with four trapezoids constructed by the four adjacent subintervals. The "bases" are given by the values of $H(t)$ at each pair of endpoints, and the "heights" are the lengths of the subintervals. For the integral itself, we get

$\dfrac{2+1.5}2(3-2)+\dfrac{6+2}2(5-3)+\dfrac{11+6}2(7-5)+\dfrac{15+11}2(10-7)=\dfrac{263}4$

So the average height of the tree (in meters) is

$\displaystyle\frac1{10-2}\int_2^{10}H(t)\,\mathrm dt\approx\frac{263}{32}$

d) When $G=50$ , the diameter of the base can be determined to be

$50=\dfrac{100x}{1+x}\implies x=1$

We're told that $\dfrac{\mathrm dx}{\mathrm dt}=0.03$ . $G$ is a function of $x$ which is in turn a function of $t$ , so when we differentiate, we use the chain rule:

$\dfrac{\mathrm dG}{\mathrm dt}=\dfrac{\mathrm dG}{\mathrm dx}\cdot\dfrac{\mathrm dx}{\mathrm dt}$

$\implies\dfrac{\mathrm dG}{\mathrm dt}=\dfrac{100}{(1+x)^2}\cdot\dfrac3{100}=\dfrac3{(1+x)^2}$

When the height of the tree is 50 meters, we found the diameter to be 1 meter, so at this point

$\dfrac{\mathrm dG}{\mathrm dt}=\dfrac34\text{ meters/year}$

4 0

2 years ago

Read 2 more answers

Which is a simplified form of the expression 2(5x + 1) – 3x?

Oksana_A [137]

Answer:

7x + 2 is your answer.

Step-by-step explanation:

2(5x + 1) – 3x

10x + 2 - 3x

7x + 2

7x + 2 is your answer.

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3 years ago

Write an equation of a line that has a y-intercept at (0, -6)

galben [10]

Answer:

$y=x-6$

Step-by-step explanation:

First to write this equation you will need to know slope intercept form which is the equation that the people that wrote this problem are presumably looking for. Slope intercept form can be simply written as $y=mx+b$ . The variable $m$ would be the slope while the variable $b$ would be the y -intercept.

So to find out this we would have to assume that m or the slope would have to be 1 so we would have $y=1x+b$ or $y=x+b$ .

Now we have the first half of the equation we can move on to the variable $b$ or the y-intercept (0,-6) . To find the variable $b$ we will just have to graph the point (0,-6) which as you can see from the picture is the y-intercept and that is -6 units below 0. So the final answer will be $y=x-6$

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2 years ago

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How can i get the volume??

Paladinen [302]

Length times width times height gives you the volume of things

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3 years ago

Can I please get some help with this :D

Luba_88 [7]

1. Anwser=53.3 (do 40*3 then anwser x 4)
2anwser=120

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2 years ago